I find the embouchure problem you describe to be the most common with
which I have dealt in 2 decades of teaching. Bill Pfund, my teacher in
doctoral school, called it "the peach-pit chin" because the chin looks
like a peach pit. You are correct: the bunched chin renders those muscles
ineffective. Moreover, it most often results from (or is caused by) the
corners pulling back or smiling excessively.

I find that the following remedy works well for this problem:

1. Buzz long tones (start with 4 beats; add more as strength improves)
on the mouthpiece and in front of a mirror. Keep chin flat (or down.)

2. Again on the mouthpiece, make a "siren" sound. As you ascend, focus
the corners to the center of the embouchure. This is more of a perception
issue than a reality. The tendency is for the corners to stretch as you
ascend. You want to resist that trend.

3. Once you can do both of those exercises with relative success, try
buzzing a scale up and down on the mouthpiece.

4. Then play simple melodies (like Getchell or the easier Concone).

It is most important to rest frequently in this process. You have muscles
that are not used to being involved. They will become somewhat sore. You
must give them refresh time.

The chin acts a s a counterbalance to the corners. If the muscles therein
don't work well, the embouchure will be unstable.